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Past talks for Fall 2010

**October 4, 2010 **

Speaker: Andrejs Treibergs, Department of Mathematics
University of Utah

**Title:
**Elastic Rings and Nanotubes

**Abstract: ** This is joint work with Feng Liu, Department of Materials Science
and Engineering. Engineers are interested in the deformation of
carbon nanotubes under hydrostatic pressure. A cross section of
the tube can be modeled as an elastic ring, which is a classical
geometric variational problem from mechanics. I'll describe the
variational problem and deduce the modulus of compression.

**October 18, 2010 **

Speaker: Grzegorz Dzierzanowski , Faculty of Civil Engineering, Warsaw Technical University

**Title:
**Bounds on the effective isotropic moduli of thin elastic composite plates

**Abstract: ** The main aim of the research is to estimate the effective
moduli of an isotropic elastic composite analyzed within the framework
of the Kirchhoff-Love theory of thin plates in bending. Results of
calculations provide explicit functional correlations between
homogenized properties of a composite plate made of two isotropic
materials thus yielding more restrictive bounds on pairs of effective
moduli than the classical (uncoupled) Hashin-Shtrikman-Walpole ones.
Applying the static-geometric analogy of Lurie and Goldenveizer enables
rewriting these new bounds in the two-dimensional elasticity (plane
stress) setting thus revealing a link to the formulae previously found
by Gibiansky and Cherkaev. Consequently, simple cross-property estimates
are proposed for the plate subject to the simultaneous bending and
in-plane loads.

**December 10, 2010 **

Speaker: Kui Ren, Department of Mathematics
University of Texas at Austin

**Title:
**Quantitative photoacoustic imaging of multiple coeffcients with
multiwavelength data

**Abstract: ** The objective of quantitative photoacoustic tomography (qPAT) is the reconstruct various physical
parameters of tissues from interior data on absorbed radiation. We generalize the results of Bal
and Uhlmann (Bal & Uhlmann, Inverse Problems, 2010) to the problem of reconstructing simultaneously
the Gruneisen, absorption and diffusion coefficients using data collected from illuminations
of different wavelengths. We prove uniqueness and stability of the inverse problem. Numerical
simulations based on a non-iterative procedure will be presented. Part of the talk is based on joint
work with Guillaume Bal.

155 South 1400 East, Room 233, Salt Lake City, UT
84112-0090, T:+1 801 581 6851, F:+1 801 581 4148